Transformer modelling in EMTP® should always start from the purpose of the study. A model that is suitable for transformer energisation or ferroresonance may not be suitable for lightning surges or very-fast-front transients. The right question is therefore not “which transformer model is best?” but “which physical effects must be represented for this transient?”
Transformers are among the hardest components to represent in electromagnetic-transient (EMT) studies: their response depends strongly on the frequency range of the disturbance and on the dominant physical effect active in that range. A model that is correct for one study can be badly wrong for another — there is no universal “transformer model”, only the model that correctly reproduces the physics that matters for the study at hand.
This page is the roadmap for the series. It sets out the overall model-selection logic; the detailed low-frequency models, high-frequency models, EMTP® transformer devices and instrument-transformer models are developed in the pages that follow. The series is written around transformers, but the underlying CIGRE guidance (High-Frequency Transformer and Reactor Models for Network Studies) also covers shunt reactors: the same high-frequency principles — terminal-overvoltage response, winding resonance, capacitance-dominated behaviour and insulation-stress assessment — carry across to reactors (which EMTP® represents with its own device), although their low-frequency behaviour differs, since a reactor typically has a single winding, a gapped or air core, and does not transform voltage.
Why this matters now. Transformer transient studies have become more demanding because transformer and reactor terminals are now exposed to a wider range of overvoltage waveforms than in traditional networks. Gas-insulated switchgear, cable-dominated networks, vacuum circuit breakers, renewable generation and altered grid configurations can produce faster-fronted or resonant voltage stresses — including stresses that fall outside the standard lightning and switching impulse tests — and these are often not represented adequately by a standard low-frequency transformer model. CIGRE notes that such conditions can place more severe stress on the insulation, particularly the internal winding insulation, which is why model choice must follow the transient rather than habit.
Key takeaway
- Choose the transformer model from the transient being studied — not from habit or the component name.
- Low-frequency studies: leakage impedance, core saturation, residual flux and losses usually matter most.
- High-frequency studies: capacitances, travelling waves, frequency-dependent behaviour and terminal response take over.
- Internal-insulation studies: a detailed winding model or a manufacturer-supported model is normally required.
Section 2
The four frequency ranges and their dominant effects
It is convenient to divide the spectrum into four bands, each governed by a different physical mechanism:
Table 1 — Frequency bands and the dominant transformer physics in each.
| Band | Indicative Range | Dominant Physics |
|---|
| Low frequency | DC – ~1 kHz | Nonlinear magnetic core: magnetisation, saturation, sometimes hysteresis (energisation, inrush, ferroresonance, harmonics). |
| Mid frequency | ~1 kHz – ~100 kHz | Frequency dependence of leakage and magnetising parameters; winding eddy-current and stray losses; damping. |
| High frequency | ~100 kHz – ~1 MHz | Capacitances (to ground, between windings, inter-turn) and distributed winding effects begin to dominate; flux no longer fully penetrates the core. |
| Very-high frequency | > ~1 MHz | Capacitive and travelling-wave behaviour dominate completely; the winding is essentially a distributed capacitive/inductive network; the core is a barrier to flux. |
The band limits above are approximate, not hard boundaries. Where core behaviour gives way to capacitive and travelling-wave behaviour depends on the unit’s size and winding arrangement, its bushing capacitances, the terminal and grounding connections, and the surrounding network — so a layer winding and an interleaved-disc winding of the same rating can have very different transition frequencies. Match the model to the dominant frequency content of the transient, and confirm it against frequency-response or other measurements where these are available.
At low frequency the magnetic core is the key element: the magnetising characteristic is nonlinear, the core can saturate, and in some cases hysteresis and core losses must be represented (their damping decides whether a ferroresonant oscillation decays). At mid frequency the leakage and magnetising parameters become frequency-dependent, eddy currents in conductors and core add loss and damping, and skin/proximity effects begin to alter the effective winding resistance. At high and very-high frequency capacitive and distributed effects dominate: capacitances to ground, between windings, and between turns control the response, the flux does not fully penetrate the core (the core acts as a barrier and its nonlinearity becomes nearly irrelevant), and a lumped low-frequency model is simply insufficient.
Frequency-dependent behaviour
Transformer resistance, inductance and capacitance do not stay constant with frequency. A model that is valid at 50 Hz may be invalid for a surge containing hundreds of kilohertz or megahertz components — which is exactly why the model must follow the frequency range of the study.
Section 4
Air-core to core behaviour on energisation
A useful physical picture is the energisation transient. Before flux has fully entered the core, the transformer behaves more like an air-core inductance — a relatively small inductance with the response shaped by conductors and surrounding structure. Once flux fully penetrates the iron, the effective inductance becomes much larger and the losses now involve conductors, core, dielectric and tank. The transition between these regimes is captured by the air-core (saturated) slope of the \(\lambda\)–\(i\) curve — in EMTP® the saturated air-core inductance \(L_{sat}\) — the parameter that most strongly governs inrush and ferroresonance (see the Low-Frequency Models and Device Catalogue pages). Open-circuit tests typically reach only 110–115 % of nominal voltage, enough to define the saturation elbow but not the air-core slope, which is therefore often missing from data sheets (typical range 0.2–0.9 pu, default 0.3 pu) and warrants a sensitivity study.
Section 5
Model classes: black-box, white-box, grey-box
Independently of the EMTP® implementation, transformer models fall into three broad classes. In plain terms: a black-box model reproduces the measured terminal behaviour but does not show what happens inside; a white-box model represents the internal geometry and construction (mainly available to manufacturers); and a grey-box model is a compromise — a physically meaningful structure whose parameters are estimated from test or terminal data. In more detail:
- Black-box models — represent only the terminal behaviour, derived from measurements (e.g. an admittance/impedance frequency response), with no internal physical information. They are valid only over the frequency range for which they were fitted and cannot locate internal stress. Advantage: compact, system-level accuracy where measured data exist. Limitation: no access to internal voltage distribution; validity confined to the fitting range; must be passive/stable for time-domain use.
- White-box models — built from the physical construction (geometry and materials), giving access to internal quantities such as inter-turn overvoltage, flux distribution, eddy and local losses. Advantage: full internal detail, suitable for insulation design and inter-turn stress. Limitation: requires proprietary manufacturer data rarely available to the user.
- Grey-box models — a compromise: a physically meaningful topology whose parameters are obtained from terminal measurements (and/or standard tests). Advantage: physical interpretability with realistically obtainable data; correct placement of the nonlinearity. Limitation: accuracy depends on the quality of the measurements and the parameter-fitting/estimation.
The EMTP® nameplate and BCTRAN transformers are essentially grey-box models (physical topology, parameters from standard tests), the instrument transformers likewise, while a black-box terminal model or a detailed white-box winding model is required at the fast-front end of the spectrum (see the High-Frequency Models page).
In practical EMTP® studies, engineers most often use matrix-based, nameplate-based or grey-box-type models, because full internal construction data is rarely available. As a general rule, treat every model as valid only over the frequency range and operating conditions (terminal and grounding state, tap position) for which it was derived, fitted or measured. This holds for all three classes but matters most for grey-box and black-box models, where extrapolating beyond the validated range can give physically misleading results.
Section 6
Modelling requirements by transient type
The following guideline table summarises how the importance of each effect varies with transient type. It should be read as a guide to which physics the chosen model must capture, not as a hard rule.
Table 2 — Importance of each transformer effect by transient type.
| Parameter / Effect | Low-Frequency | Slow-Front | Fast-Front | Very-Fast-Front |
|---|
| Short-circuit impedance | Very important | Very important | Important | Usually negligible |
| Saturation | Very important | Important | Usually negligible | Negligible |
| Iron losses | Important (some cases) | Usually negligible | Negligible | Negligible |
| Eddy currents | Very important | Important | Usually negligible | Usually negligible |
| Capacitive coupling | Usually negligible | Important | Very important | Very important |
Exceptions exist: capacitances can matter in certain ferroresonance cases, and saturation may be unimportant in some harmonic or controller-interaction studies. The model should therefore be selected by the physical behaviour to be represented, not by the component name.
The same logic can be read the other way round — from the study objective to a suitable starting model and its main limitation:
Table 3 — Practical EMTP® transformer model selection by study objective.
| Study Objective | Main Physical Effect | Suitable EMTP® Approach | Main Limitation |
|---|
| Energisation / inrush | Core saturation and residual flux | Nameplate transformer or nonlinear low-frequency model | Accuracy depends on saturation data and initial flux |
| Ferroresonance | Saturation, losses and system capacitance | Nonlinear transformer with appropriate capacitances | Sensitive to losses, switching condition and initial state |
| Harmonic / low-frequency interaction | Leakage impedance and magnetising branch | BCTRAN or nameplate-input transformer | Mainly valid for low-frequency studies |
| Lightning / fast-front surge at terminals | Capacitance and surge impedance | Terminal capacitance, FDB or black-box model | Does not show internal inter-turn stress |
| Internal winding insulation stress | Travelling waves and inter-turn voltage distribution | Detailed winding model or manufacturer model | Requires winding geometry and specialist data |
| CT / VT / CVT transient response | Burden, saturation, remanence and divider dynamics | EMTP® instrument-transformer devices | Requires correct burden and excitation data |
Important modelling note
Standard EMTP® transformer models such as BCTRAN and the nameplate-input transformers are intended for low-frequency and power-frequency transient studies. For fast-front or very-fast-front studies, winding capacitances, frequency-dependent terminal behaviour or a detailed winding model may be required. Applying a low-frequency transformer model directly to a lightning or very-fast-front study is one of the most common modelling errors.
Section 8
Practical model-selection questions
Before choosing a model, answer the following:
- What is the transient type? (energisation/inrush, ferroresonance, harmonics, slow-front switching, lightning/fast front, very-fast front)
- What is the dominant frequency range? (low, mid, high, very-high)
- Is saturation important? (energisation, inrush, ferroresonance → yes; some harmonic/controller studies → perhaps not)
- Are winding capacitances important? (fast/very-fast fronts, capacitive transfer → yes)
- Is the concern terminal-only behaviour, or internal stress? (system interaction → terminal model; inter-turn insulation → internal/white-box model)
- What data are available? (nameplate/standard tests → nameplate or BCTRAN; frequency-response data → black-box; geometry → white-box)
- Is a manufacturer-supported model required? (inter-turn insulation coordination, internal resonance, design validation)
- Has the model been validated, and over what range? (for fast-front and high-frequency work a model is only trustworthy where it has been checked against measurement — frequency response/FRA, terminal admittance or voltage-transfer data — since calculated resonance frequencies and waveshapes are unreliable until confirmed)
The answers point directly to a device in the EMTP® library: nameplate-input or BCTRAN for low-frequency, saturation-driven and multi-winding studies (the Low-Frequency Models and Device Catalogue pages); these supplemented with capacitances/FDB or a detailed winding model for fast fronts (the High-Frequency Models page); and the dedicated CT/VT/CVT devices for instrument-transformer studies (the Instrument Transformers page).
Common modelling mistakes to avoid:
- using a low-frequency transformer model for lightning or fast-front surge studies;
- using a terminal model to assess internal winding stress;
- ignoring saturation and residual flux in energisation and inrush studies;
- using an ideal transformer where leakage impedance, losses or inrush current actually matter.
In summary, the key decision is not whether the transformer can be represented in EMTP® — it almost always can — but whether the chosen model carries the physical effects that govern the transient under study. As the key takeaway set out, that means leakage impedance, saturation, residual flux and losses at low frequency, and winding capacitances, terminal frequency response and damping at high frequency; and where internal insulation stress must be assessed, a terminal model is never enough — a winding-level representation or a validated manufacturer-supported model is required. The remaining pages take each of these regimes in turn: low-frequency models, high-frequency models, the EMTP® device catalogue, and instrument transformers.
